In order to solve the problems of establishing complex acceleration model in accelerated life test under multi-stress conditions, the model parameters are difficult to solve and the stress coupling problem is usually neglected in the modeling process, an improved BP neural network model is established according to beetle antennae search (BAS). The BAS-BP neural network model was trained using the failure data of the 4 sets of stress levels collected in the multi-stress accelerated life test to predict the reliability and failure time of the 5th set of stress levels. The prediction results of the model were evaluated by using the average relative error and the goodness of fit, and compared with the prediction results of BP neural network. The results show that the BAS-BP neural network has better accuracy and robustness.